In order to plan an orthodontic treatment for repositioning a patient's teeth, it is often necessary to articulate the patient's arches in digital space to match a same relative alignment as in the patient's mouth. The arches include a maxillary arch and a mandibular arch that make up the top and bottom portions of the patient's mouth, respectively. The maxillary arch is a curved ridge of the upper jaw bone (i.e., the roof of the patient's mouth), whereas the mandibular arch is a curved ridge of the lower jaw bone (i.e., the arch under the patient's tongue). When dental models of the opposing arches are digitally scanned, each model is scanned and saved as a separate virtual model. The digital scans can be used to determine a treatment plan based on the positions of the patient's teeth, as well as the patient's jaw alignment, for example. The scanning of the dental models can be done using existing CAD software to manually articulate the arches and align the models. However, the manual process can be tedious as well as time consuming, and important information regarding the arch alignments may be lost using the existing scanning technologies.